Rockfish Historical Harvest Estimates

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: *rf_harvest_est_nm_wt_thru2023_8e+06__2025-07-16* (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9976

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Model fit

Logbook residuals

Figure 18.- Residuals from logbook harvests.

SWHS residuals

Figure 19.- Residuals from SWHS harvests.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 21.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Weight Fits

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

### Summary of unconverged parameters:

Table X. Unconverged parameters.

area	variable	year	user	species	Rhat
BSAI	Ro_ayu	2			1.244275
BSAI	Ro_ay	2			1.241290
BSAI	Ro_ayu	38			1.239584
BSAI	Ro_ay	38			1.238576
BSAI	Ry_ayu	4			1.237982
BSAI	Ro_ayu	16			1.235717
BSAI	Ry_ay	4			1.230923
BSAI	Ro_ay	16			1.226588
BSAI	Ry_ayu	2			1.225121
BSAI	Ry_ayg	8			1.223901
BSAI	Ry_ay	2			1.220207
BSAI	Ry_ayu	19			1.216825
BSAI	Ry_ayu	18			1.216508
BSAI	Ro_ayu	5			1.214192
BSAI	Ry_ay	19			1.210052
BSAI	Ro_ayu	33			1.209743
BSAI	Ro_ay	5			1.209644
BSAI	Ry_ay	18			1.208876
BSAI	Ry_ayu	9			1.205798
BSAI	Ro_ayu	46			1.205573
BSAI	Ro_ay	33			1.200549
BSAI	Ro_ay	46			1.197774
BSAI	Ry_ayu	21			1.197014
BSAI	Ry_ay	9			1.195172
BSAI	Ry_ay	21			1.191088
BSAI	Ry_ayu	5			1.190707
BSAI	Ro_ayu	22			1.188432
BSAI	Ro_ayu	36			1.185198
BSAI	Ry_ayu	7			1.183268
BSAI	Ro_ay	22			1.182635
BSAI	Ry_ayg	12			1.180601
BSAI	Ry_ay	5			1.178877
BSAI	Ro_ay	36			1.178856
BSAI	Ry_ay	7			1.178334
BSAI	Ro_ayu	32			1.176965
BSAI	Ry_ayu	30			1.175425
BSAI	Ro_ayu	4			1.174654
BSAI	Ry_ay	30			1.172118
BSAI	Ro_ay	32			1.168693
BSAI	Ro_ayu	11			1.166959
BSAI	Ry_ayg	1			1.164355
BSAI	Ro_ayu	35			1.158675
BSAI	Ro_ayu	40			1.153805
BSAI	Ro_ay	35			1.153464
BSAI	Ry_ayu	31			1.153202
BSAI	Ro_ay	11			1.153101
BSAI	Ry_ay	31			1.150582
BSAI	Ro_ayu	8			1.150438
BSAI	Ro_ay	4			1.149196
BSAI	Ro_ay	8			1.147140
BSAI	Ro_ayu	13			1.146471
BSAI	Ro_ay	40			1.145642
BSAI	Ry_ayu	8			1.142614
BSAI	Ry_ayu	36			1.140086
BSAI	Ry_ayu	1			1.139539
BSAI	Ro_ay	13			1.139074
BSAI	Ry_ay	8			1.138500
BSAI	Ry_ay	36			1.135567
BSAI	Ro_ayu	24			1.128154
BSAI	Ro_ay	24			1.125215
BSAI	Ry_ay	1			1.122622
BSAI	Ro_ayu	34			1.120564
BSAI	Ro_ay	34			1.116610
BSAI	Ry_ayu	47			1.115822
BSAI	Ry_ay	47			1.113904
BSAI	Ro_ayu	17			1.113778
BSAI	Ro_ayu	30			1.111816
CI	mu_beta1_yellow				1.235253
CI	Ro_ayu	13			1.137029
CI	tau_beta4_pH			2	1.119611
CSEO	pH	44	2	2	1.170614
CSEO	pH	47	2	2	1.162234
CSEO	pH	46	2	2	1.139966
CSEO	pH	45	2	2	1.125140
EWYKT	p_dsr	6	1		1.280859
EWYKT	p_dsr	3	1		1.275604
EWYKT	p_dsr	1	1		1.248123
EWYKT	p_dsr	25	1		1.238803
EWYKT	p_dsr	23	1		1.213375
EWYKT	p_dsr	3	2		1.201601
EWYKT	p_dsr	18	1		1.187125
EWYKT	Rs_ayu	18			1.182964
EWYKT	p_dsr	10	1		1.156270
EWYKT	Rs_ayu	34			1.153794
EWYKT	p_dsr	11	1		1.148267
EWYKT	p_dsr	13	1		1.146192
EWYKT	p_dsr	16	2		1.146034
EWYKT	p_dsr	21	1		1.144607
EWYKT	p_dsr	16	1		1.144125
EWYKT	p_dsr	5	1		1.142451
EWYKT	p_dsr	14	1		1.141730
EWYKT	p_dsr	14	2		1.140508
EWYKT	Rs_ay	34			1.140425
EWYKT	p_dsr	7	1		1.133794
EWYKT	p_dsr	2	2		1.123613
EWYKT	p_dsr	26	1		1.122963
EWYKT	beta1_dsr				1.120842
EWYKT	p_dsr	11	2		1.112071
EWYKT	p_dsr	29	1		1.110788
NG	mu_beta1_black				1.255389
NSEO	Rs_ayu	3			1.207382
NSEO	Ro_ayu	3			1.166754
NSEO	Rs_ay	3			1.155944
NSEO	Rdnye_ayu	3			1.149303
NSEO	Ro_ayu	6			1.128119
NSEO	Rdnye_ayu	6			1.127663
PWSI	beta1_pH			2	1.292117
PWSI	beta2_yellow				1.113476
PWSO	beta1_pH			2	1.282064
SOKO2SAP	Ro_ayu	13			1.285389
SOKO2SAP	Ro_ayu	10			1.284920
SOKO2SAP	Ro_ay	13			1.284904
SOKO2SAP	Ro_ay	10			1.283476
SOKO2SAP	Ro_ayu	4			1.281284
SOKO2SAP	Ro_ay	4			1.278849
SOKO2SAP	Ro_ayu	2			1.275115
SOKO2SAP	Ro_ayu	5			1.274537
SOKO2SAP	Ro_ay	5			1.273568
SOKO2SAP	Ro_ay	2			1.272404
SOKO2SAP	Ro_ayu	11			1.258030
SOKO2SAP	Ro_ay	11			1.248292
SOKO2SAP	Ro_ayu	27			1.247815
SOKO2SAP	Ro_ay	27			1.245610
SOKO2SAP	Ro_ayu	18			1.240223
SOKO2SAP	Ro_ay	18			1.234304
SOKO2SAP	Ro_ayg	2			1.216547
SOKO2SAP	Ro_ayu	3			1.208009
SOKO2SAP	Ro_ay	3			1.204339
SOKO2SAP	Ro_ayu	24			1.204064
SOKO2SAP	Ro_ay	24			1.199930
SOKO2SAP	beta1_pH			3	1.199112
SOKO2SAP	Ro_ayu	7			1.190101
SOKO2SAP	Ro_ay	7			1.182915
SOKO2SAP	Ro_ayu	14			1.158316
SOKO2SAP	Ro_ayu	47			1.156556
SOKO2SAP	Ro_ayu	12			1.154466
SOKO2SAP	Ro_ay	47			1.151455
SOKO2SAP	Ro_ay	14			1.150252
SOKO2SAP	Ry_ayu	20			1.150040
SOKO2SAP	Ro_ay	12			1.146542
SOKO2SAP	Ry_ay	20			1.146312
SOKO2SAP	Ho_ayg	11			1.140103
SSEI	pH	47	2	2	1.167394
SSEI	pH	45	2	2	1.142865
SSEI	beta2_pelagic				1.134296
SSEI	pH	46	2	2	1.127772
SSEI	pH	44	2	2	1.119743
SSEO	Rs_ayu	9			1.136294
SSEO	Rs_ayu	1			1.121169
WKMA	Ry_ayu	28			1.153515
WKMA	Ro_ayu	11			1.153070
WKMA	Rb_ayu	3			1.148986
WKMA	Rp_ayu	3			1.147177
WKMA	Ry_ayu	9			1.139976
WKMA	Ro_ay	11			1.139669
WKMA	Ry_ay	28			1.137257
WKMA	Ro_ayu	7			1.134113
WKMA	Ro_ay	7			1.126586
afognak	Ry_ayu	21			1.113908
afognak	Ry_ay	21			1.112291
afognak	Ro_ayu	22			1.112185
eastside	Ho_ayu	5			1.176631
eastside	Ho_ayu	20			1.128519
eastside	Ro_ayu	21			1.125421
eastside	Hy_ayu	20			1.123959
eastside	Ry_ayu	3			1.117163
eastside	Ry_ay	3			1.113732
northeast	Ro_ayu	1			1.114103

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.126	0.073	-0.266	-0.128	0.030
mu_bc_H[2]	-0.095	0.045	-0.173	-0.099	0.004
mu_bc_H[3]	-0.432	0.070	-0.561	-0.435	-0.289
mu_bc_H[4]	-0.987	0.192	-1.368	-0.983	-0.613
mu_bc_H[5]	0.911	0.997	-0.170	0.714	3.287
mu_bc_H[6]	-2.135	0.320	-2.754	-2.143	-1.501
mu_bc_H[7]	-0.457	0.109	-0.677	-0.457	-0.244
mu_bc_H[8]	0.262	0.366	-0.340	0.219	1.101
mu_bc_H[9]	-0.289	0.134	-0.553	-0.288	-0.020
mu_bc_H[10]	-0.101	0.070	-0.230	-0.104	0.044
mu_bc_H[11]	-0.123	0.037	-0.197	-0.123	-0.050
mu_bc_H[12]	-0.254	0.105	-0.477	-0.249	-0.053
mu_bc_H[13]	-0.137	0.078	-0.283	-0.140	0.022
mu_bc_H[14]	-0.303	0.096	-0.496	-0.300	-0.122
mu_bc_H[15]	-0.343	0.050	-0.440	-0.344	-0.243
mu_bc_H[16]	-0.262	0.375	-0.897	-0.291	0.571
mu_bc_R[1]	1.312	0.139	1.041	1.308	1.594
mu_bc_R[2]	1.455	0.092	1.271	1.456	1.632
mu_bc_R[3]	1.389	0.144	1.102	1.393	1.654
mu_bc_R[4]	0.911	0.205	0.481	0.917	1.299
mu_bc_R[5]	1.194	0.465	0.296	1.184	2.086
mu_bc_R[6]	-1.608	0.416	-2.455	-1.591	-0.833
mu_bc_R[7]	0.436	0.207	0.005	0.442	0.832
mu_bc_R[8]	0.537	0.188	0.163	0.538	0.894
mu_bc_R[9]	0.331	0.206	-0.132	0.348	0.684
mu_bc_R[10]	1.307	0.170	0.964	1.314	1.620
mu_bc_R[11]	1.038	0.098	0.845	1.040	1.232
mu_bc_R[12]	0.820	0.206	0.392	0.822	1.221
mu_bc_R[13]	1.026	0.101	0.823	1.028	1.220
mu_bc_R[14]	0.894	0.144	0.608	0.896	1.177
mu_bc_R[15]	0.784	0.109	0.567	0.784	1.002
mu_bc_R[16]	1.091	0.126	0.839	1.094	1.331
tau_pH[1]	5.128	0.440	4.299	5.113	6.017
tau_pH[2]	1.980	0.222	1.566	1.971	2.439
tau_pH[3]	2.144	0.223	1.744	2.135	2.613
beta0_pH[1,1]	0.555	0.179	0.190	0.560	0.891
beta0_pH[2,1]	1.367	0.182	0.993	1.371	1.714
beta0_pH[3,1]	1.421	0.203	0.960	1.432	1.776
beta0_pH[4,1]	1.562	0.221	1.108	1.577	1.957
beta0_pH[5,1]	-0.858	0.286	-1.482	-0.839	-0.360
beta0_pH[6,1]	-0.729	0.519	-2.006	-0.635	-0.049
beta0_pH[7,1]	-0.498	0.588	-1.921	-0.440	0.510
beta0_pH[8,1]	-0.676	0.305	-1.363	-0.636	-0.194
beta0_pH[9,1]	-0.629	0.276	-1.222	-0.612	-0.152
beta0_pH[10,1]	0.349	0.207	-0.095	0.355	0.725
beta0_pH[11,1]	-0.078	0.167	-0.424	-0.071	0.237
beta0_pH[12,1]	0.490	0.189	0.112	0.493	0.851
beta0_pH[13,1]	0.005	0.146	-0.290	0.004	0.293
beta0_pH[14,1]	-0.314	0.169	-0.654	-0.310	-0.006
beta0_pH[15,1]	-0.029	0.184	-0.398	-0.029	0.314
beta0_pH[16,1]	-0.477	0.364	-1.397	-0.415	0.056
beta0_pH[1,2]	2.828	0.162	2.498	2.836	3.132
beta0_pH[2,2]	2.891	0.137	2.616	2.891	3.163
beta0_pH[3,2]	3.136	0.155	2.850	3.130	3.462
beta0_pH[4,2]	2.951	0.132	2.690	2.952	3.216
beta0_pH[5,2]	4.768	1.372	2.979	4.500	8.307
beta0_pH[6,2]	3.115	0.208	2.716	3.117	3.524
beta0_pH[7,2]	1.834	0.196	1.450	1.833	2.218
beta0_pH[8,2]	2.875	0.177	2.535	2.875	3.229
beta0_pH[9,2]	3.440	0.228	2.998	3.433	3.894
beta0_pH[10,2]	3.687	0.210	3.293	3.681	4.105
beta0_pH[11,2]	-4.839	0.311	-5.467	-4.836	-4.255
beta0_pH[12,2]	-4.783	0.392	-5.573	-4.767	-4.044
beta0_pH[13,2]	-4.586	0.399	-5.355	-4.589	-3.782
beta0_pH[14,2]	-5.588	0.477	-6.566	-5.573	-4.733
beta0_pH[15,2]	-4.296	0.343	-4.939	-4.302	-3.620
beta0_pH[16,2]	-4.870	0.388	-5.682	-4.857	-4.113
beta0_pH[1,3]	-0.141	0.702	-1.753	-0.044	1.006
beta0_pH[2,3]	2.189	0.162	1.873	2.190	2.501
beta0_pH[3,3]	2.534	0.153	2.238	2.533	2.826
beta0_pH[4,3]	2.967	0.159	2.664	2.965	3.284
beta0_pH[5,3]	2.146	1.357	0.426	1.863	5.768
beta0_pH[6,3]	1.002	0.507	-0.206	1.037	1.870
beta0_pH[7,3]	0.631	0.173	0.304	0.629	0.974
beta0_pH[8,3]	0.311	0.195	-0.058	0.309	0.701
beta0_pH[9,3]	-0.645	0.393	-1.660	-0.606	0.002
beta0_pH[10,3]	0.458	0.401	-0.542	0.510	1.076
beta0_pH[11,3]	-0.150	0.333	-0.758	-0.164	0.530
beta0_pH[12,3]	-0.857	0.352	-1.609	-0.825	-0.243
beta0_pH[13,3]	-0.120	0.312	-0.722	-0.122	0.499
beta0_pH[14,3]	-0.270	0.257	-0.747	-0.277	0.265
beta0_pH[15,3]	-0.716	0.301	-1.334	-0.709	-0.161
beta0_pH[16,3]	-0.392	0.295	-0.977	-0.395	0.184
beta1_pH[1,1]	3.077	0.321	2.495	3.060	3.768
beta1_pH[2,1]	2.154	0.280	1.663	2.136	2.753
beta1_pH[3,1]	1.982	0.327	1.424	1.956	2.735
beta1_pH[4,1]	2.404	0.355	1.836	2.359	3.230
beta1_pH[5,1]	2.288	0.353	1.711	2.247	3.055
beta1_pH[6,1]	3.827	1.134	2.327	3.571	6.614
beta1_pH[7,1]	2.593	1.156	0.740	2.464	5.398
beta1_pH[8,1]	4.076	1.056	2.640	3.848	6.730
beta1_pH[9,1]	2.305	0.362	1.708	2.272	3.105
beta1_pH[10,1]	2.223	0.300	1.696	2.211	2.857
beta1_pH[11,1]	3.259	0.210	2.858	3.258	3.677
beta1_pH[12,1]	2.543	0.223	2.130	2.536	2.982
beta1_pH[13,1]	2.975	0.215	2.559	2.969	3.412
beta1_pH[14,1]	3.413	0.220	3.003	3.407	3.862
beta1_pH[15,1]	2.533	0.234	2.095	2.530	3.007
beta1_pH[16,1]	4.124	0.688	3.193	3.983	5.764
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.001	0.038	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.001	0.000	0.000	0.000
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.683	0.344	6.026	6.677	7.373
beta1_pH[12,2]	6.448	0.456	5.607	6.430	7.372
beta1_pH[13,2]	6.962	0.446	6.093	6.965	7.838
beta1_pH[14,2]	7.222	0.501	6.313	7.206	8.237
beta1_pH[15,2]	6.777	0.372	6.044	6.777	7.496
beta1_pH[16,2]	7.464	0.432	6.641	7.452	8.360
beta1_pH[1,3]	4.679	1.619	2.137	4.483	8.046
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	3.904	6.664	0.840	2.803	13.284
beta1_pH[6,3]	3.414	8.075	0.407	2.622	9.233
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	2.744	0.355	2.072	2.742	3.440
beta1_pH[9,3]	2.764	0.468	1.992	2.723	3.918
beta1_pH[10,3]	2.923	0.474	2.129	2.867	4.024
beta1_pH[11,3]	2.740	0.391	1.962	2.737	3.478
beta1_pH[12,3]	4.111	0.442	3.299	4.094	5.005
beta1_pH[13,3]	1.702	0.335	1.044	1.695	2.357
beta1_pH[14,3]	2.518	0.330	1.850	2.519	3.178
beta1_pH[15,3]	2.001	0.325	1.393	1.988	2.662
beta1_pH[16,3]	1.803	0.327	1.168	1.803	2.445
beta2_pH[1,1]	0.479	0.126	0.294	0.463	0.766
beta2_pH[2,1]	0.586	0.405	0.250	0.517	1.278
beta2_pH[3,1]	0.656	0.467	0.224	0.562	1.768
beta2_pH[4,1]	0.480	0.210	0.208	0.445	0.954
beta2_pH[5,1]	1.452	0.958	0.258	1.305	3.742
beta2_pH[6,1]	0.183	0.066	0.086	0.174	0.336
beta2_pH[7,1]	0.053	0.440	0.000	0.000	0.290
beta2_pH[8,1]	0.240	0.091	0.117	0.224	0.454
beta2_pH[9,1]	0.441	0.228	0.180	0.403	0.934
beta2_pH[10,1]	0.614	0.299	0.274	0.559	1.285
beta2_pH[11,1]	0.787	0.213	0.477	0.753	1.299
beta2_pH[12,1]	1.349	0.475	0.743	1.253	2.528
beta2_pH[13,1]	0.739	0.233	0.420	0.705	1.261
beta2_pH[14,1]	0.839	0.211	0.527	0.808	1.337
beta2_pH[15,1]	0.805	0.357	0.413	0.747	1.468
beta2_pH[16,1]	0.379	0.171	0.169	0.333	0.825
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-1.984	1.823	-6.741	-1.480	-0.029
beta2_pH[4,2]	-1.958	1.804	-6.657	-1.474	-0.030
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.554	4.462	-20.609	-8.465	-4.074
beta2_pH[12,2]	-8.064	5.092	-20.450	-7.125	-1.030
beta2_pH[13,2]	-7.932	5.072	-20.788	-6.828	-1.643
beta2_pH[14,2]	-8.598	4.857	-21.139	-7.475	-2.534
beta2_pH[15,2]	-9.318	4.531	-21.213	-8.266	-3.774
beta2_pH[16,2]	-9.621	4.418	-20.638	-8.678	-3.981
beta2_pH[1,3]	0.244	0.341	0.101	0.178	0.664
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	8.964	6.455	-0.182	7.995	24.171
beta2_pH[6,3]	9.068	6.285	0.174	8.169	23.703
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	9.959	5.721	1.754	8.762	23.387
beta2_pH[9,3]	8.913	6.240	0.482	7.835	23.513
beta2_pH[10,3]	8.477	6.517	0.471	7.601	23.287
beta2_pH[11,3]	-2.397	2.334	-9.467	-1.741	-0.600
beta2_pH[12,3]	-2.504	2.105	-8.619	-1.882	-0.953
beta2_pH[13,3]	-2.948	2.493	-10.455	-2.160	-0.765
beta2_pH[14,3]	-2.942	2.478	-10.762	-2.149	-0.914
beta2_pH[15,3]	-3.060	2.427	-10.116	-2.266	-0.990
beta2_pH[16,3]	-3.081	2.534	-10.111	-2.274	-0.925
beta3_pH[1,1]	35.948	0.839	34.391	35.929	37.636
beta3_pH[2,1]	33.552	1.172	31.463	33.477	36.104
beta3_pH[3,1]	33.629	1.083	31.517	33.632	35.850
beta3_pH[4,1]	33.858	1.219	31.636	33.781	36.446
beta3_pH[5,1]	27.672	1.035	26.448	27.465	30.705
beta3_pH[6,1]	38.248	3.256	32.143	38.097	44.694
beta3_pH[7,1]	30.621	8.005	18.511	29.884	44.998
beta3_pH[8,1]	40.072	2.155	36.353	39.794	44.927
beta3_pH[9,1]	30.704	1.491	28.151	30.631	34.004
beta3_pH[10,1]	32.966	1.012	31.155	32.902	35.073
beta3_pH[11,1]	30.327	0.469	29.416	30.324	31.270
beta3_pH[12,1]	30.163	0.406	29.368	30.162	30.967
beta3_pH[13,1]	33.178	0.583	32.068	33.175	34.375
beta3_pH[14,1]	32.018	0.471	31.131	32.022	32.984
beta3_pH[15,1]	31.203	0.638	29.986	31.203	32.484
beta3_pH[16,1]	32.076	1.137	30.274	31.919	34.627
beta3_pH[1,2]	30.055	7.972	18.410	28.987	44.853
beta3_pH[2,2]	30.066	7.940	18.525	29.041	44.947
beta3_pH[3,2]	29.865	7.937	18.503	28.966	44.901
beta3_pH[4,2]	30.104	7.962	18.528	28.976	44.995
beta3_pH[5,2]	30.124	8.033	18.579	29.178	45.082
beta3_pH[6,2]	30.060	7.970	18.453	29.141	44.861
beta3_pH[7,2]	29.776	7.912	18.573	28.700	44.999
beta3_pH[8,2]	29.882	7.975	18.383	28.832	44.833
beta3_pH[9,2]	29.872	7.991	18.447	28.890	44.937
beta3_pH[10,2]	30.056	7.927	18.521	29.152	45.004
beta3_pH[11,2]	43.407	0.180	43.119	43.387	43.787
beta3_pH[12,2]	43.195	0.195	42.935	43.146	43.739
beta3_pH[13,2]	43.872	0.143	43.496	43.910	44.042
beta3_pH[14,2]	43.303	0.206	43.045	43.251	43.797
beta3_pH[15,2]	43.407	0.189	43.107	43.386	43.798
beta3_pH[16,2]	43.493	0.188	43.157	43.492	43.839
beta3_pH[1,3]	39.110	3.217	32.617	38.989	45.280
beta3_pH[2,3]	30.037	7.947	18.562	29.151	44.866
beta3_pH[3,3]	30.264	8.032	18.503	29.344	44.993
beta3_pH[4,3]	30.379	7.922	18.474	29.820	44.794
beta3_pH[5,3]	36.674	3.920	31.238	36.034	45.065
beta3_pH[6,3]	40.409	3.519	32.020	40.770	45.660
beta3_pH[7,3]	38.193	4.388	31.279	37.988	45.590
beta3_pH[8,3]	41.495	0.252	41.061	41.493	41.947
beta3_pH[9,3]	33.458	0.579	31.655	33.558	34.210
beta3_pH[10,3]	35.805	0.835	33.351	36.009	36.863
beta3_pH[11,3]	41.767	0.825	40.042	41.821	43.204
beta3_pH[12,3]	41.726	0.380	40.973	41.742	42.480
beta3_pH[13,3]	42.727	0.887	41.034	42.710	44.809
beta3_pH[14,3]	41.099	0.585	39.871	41.132	42.171
beta3_pH[15,3]	42.640	0.657	41.176	42.738	43.719
beta3_pH[16,3]	42.903	0.729	41.273	43.005	44.153
beta4_pH[1,1]	0.930	0.750	-0.108	0.823	2.682
beta4_pH[2,1]	1.212	1.049	-0.003	0.974	3.999
beta4_pH[3,1]	0.345	0.971	-1.083	0.243	2.500
beta4_pH[4,1]	0.638	1.231	-1.281	0.508	3.625
beta4_pH[5,1]	-0.625	0.601	-1.912	-0.567	0.375
beta4_pH[6,1]	-0.655	0.588	-1.869	-0.604	0.327
beta4_pH[7,1]	0.323	1.329	-1.544	0.006	3.838
beta4_pH[8,1]	-0.058	1.013	-1.466	-0.223	2.597
beta4_pH[9,1]	0.469	1.354	-1.242	0.117	4.051
beta4_pH[10,1]	0.642	1.265	-0.644	0.229	4.154
beta4_pH[11,1]	0.742	1.462	-1.305	0.485	4.671
beta4_pH[12,1]	1.006	1.618	-1.365	0.706	5.318
beta4_pH[13,1]	1.868	1.611	-0.235	1.528	6.025
beta4_pH[14,1]	2.118	1.647	-0.117	1.765	6.201
beta4_pH[15,1]	0.371	1.237	-1.309	0.182	3.352
beta4_pH[16,1]	0.667	1.427	-1.281	0.394	4.307
beta4_pH[1,2]	-3.263	0.852	-3.963	-3.458	-0.798
beta4_pH[2,2]	0.378	1.952	-1.910	-0.165	5.579
beta4_pH[3,2]	-0.948	2.146	-3.291	-1.616	4.811
beta4_pH[4,2]	1.604	2.008	-0.994	1.133	6.527
beta4_pH[5,2]	0.059	2.336	-3.545	-0.254	5.453
beta4_pH[6,2]	-0.301	2.437	-3.810	-0.630	5.318
beta4_pH[7,2]	0.087	0.958	-1.759	0.085	1.972
beta4_pH[8,2]	-0.773	2.153	-3.446	-1.311	4.860
beta4_pH[9,2]	-0.175	2.420	-3.735	-0.521	5.386
beta4_pH[10,2]	-2.385	2.142	-3.986	-3.421	3.428
beta4_pH[11,2]	-0.462	0.626	-1.340	-0.548	0.918
beta4_pH[12,2]	-1.083	1.054	-2.535	-1.270	1.793
beta4_pH[13,2]	-1.602	0.915	-2.882	-1.724	0.372
beta4_pH[14,2]	-0.140	1.047	-1.430	-0.361	2.690
beta4_pH[15,2]	-1.741	0.836	-2.923	-1.861	0.025
beta4_pH[16,2]	-0.879	1.050	-2.209	-1.077	1.840
beta4_pH[1,3]	-0.389	1.532	-2.265	-0.782	3.790
beta4_pH[2,3]	-1.311	0.597	-2.137	-1.404	0.100
beta4_pH[3,3]	-1.656	0.777	-2.695	-1.788	0.217
beta4_pH[4,3]	-0.309	1.404	-1.894	-0.684	3.555
beta4_pH[5,3]	0.411	1.940	-3.243	0.258	5.008
beta4_pH[6,3]	0.451	1.841	-2.720	0.237	4.802
beta4_pH[7,3]	0.346	1.756	-2.416	0.117	4.920
beta4_pH[8,3]	0.777	1.683	-1.693	0.472	5.058
beta4_pH[9,3]	0.924	1.706	-1.549	0.621	5.035
beta4_pH[10,3]	0.246	1.665	-2.169	-0.043	4.455
beta4_pH[11,3]	0.911	1.207	-0.509	0.603	4.111
beta4_pH[12,3]	0.637	1.178	-1.044	0.400	3.879
beta4_pH[13,3]	0.060	0.677	-0.915	-0.028	1.571
beta4_pH[14,3]	0.385	1.039	-1.010	0.201	3.054
beta4_pH[15,3]	0.201	0.623	-0.704	0.118	1.539
beta4_pH[16,3]	0.656	1.042	-0.575	0.402	3.650
beta0_pelagic[1]	2.225	0.131	1.961	2.227	2.479
beta0_pelagic[2]	1.511	0.126	1.261	1.510	1.760
beta0_pelagic[3]	-0.387	0.665	-1.921	-0.253	0.583
beta0_pelagic[4]	-0.442	0.854	-2.339	-0.262	0.724
beta0_pelagic[5]	1.200	0.256	0.685	1.200	1.682
beta0_pelagic[6]	1.472	0.273	0.901	1.487	1.959
beta0_pelagic[7]	1.592	0.208	1.191	1.580	2.034
beta0_pelagic[8]	1.759	0.205	1.369	1.747	2.195
beta0_pelagic[9]	2.470	0.325	1.832	2.478	3.061
beta0_pelagic[10]	2.502	0.209	2.032	2.512	2.897
beta0_pelagic[11]	0.135	0.500	-1.207	0.266	0.751
beta0_pelagic[12]	1.678	0.143	1.397	1.681	1.950
beta0_pelagic[13]	0.318	0.197	-0.099	0.326	0.670
beta0_pelagic[14]	-0.097	0.280	-0.723	-0.069	0.362
beta0_pelagic[15]	-0.258	0.141	-0.522	-0.255	0.021
beta0_pelagic[16]	0.291	0.281	-0.453	0.360	0.673
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	1.905	1.092	0.511	1.683	4.566
beta1_pelagic[4]	1.876	1.095	0.456	1.601	4.890
beta1_pelagic[5]	-0.073	0.315	-0.674	-0.066	0.546
beta1_pelagic[6]	-0.097	0.453	-0.880	-0.156	0.761
beta1_pelagic[7]	-0.013	0.288	-0.566	-0.008	0.555
beta1_pelagic[8]	-0.006	0.281	-0.567	-0.008	0.556
beta1_pelagic[9]	0.212	0.499	-0.778	0.326	0.990
beta1_pelagic[10]	0.069	0.275	-0.476	0.065	0.603
beta1_pelagic[11]	3.462	1.136	2.062	3.130	6.466
beta1_pelagic[12]	2.776	0.309	2.222	2.758	3.407
beta1_pelagic[13]	2.893	0.695	1.781	2.810	4.459
beta1_pelagic[14]	4.279	1.005	2.768	4.108	6.523
beta1_pelagic[15]	2.917	0.267	2.421	2.913	3.444
beta1_pelagic[16]	3.633	0.982	2.677	3.291	6.450
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	0.759	2.433	0.034	0.158	6.908
beta2_pelagic[4]	1.255	3.026	0.028	0.361	11.244
beta2_pelagic[5]	-0.004	0.673	-1.424	0.004	1.381
beta2_pelagic[6]	-0.083	0.699	-1.477	-0.136	1.383
beta2_pelagic[7]	0.029	0.672	-1.373	0.010	1.459
beta2_pelagic[8]	0.024	0.639	-1.317	0.019	1.390
beta2_pelagic[9]	0.187	0.686	-1.271	0.249	1.508
beta2_pelagic[10]	0.033	0.624	-1.277	0.026	1.415
beta2_pelagic[11]	2.704	4.718	0.109	0.374	16.542
beta2_pelagic[12]	6.629	5.777	1.076	4.763	22.237
beta2_pelagic[13]	1.163	2.739	0.194	0.471	9.023
beta2_pelagic[14]	0.328	0.172	0.162	0.290	0.704
beta2_pelagic[15]	7.432	6.343	1.172	5.183	23.649
beta2_pelagic[16]	5.477	6.309	0.188	3.689	22.835
beta3_pelagic[1]	29.870	8.013	18.421	28.939	44.807
beta3_pelagic[2]	29.567	7.870	18.400	28.418	44.873
beta3_pelagic[3]	29.378	6.254	19.040	28.739	43.583
beta3_pelagic[4]	24.774	4.962	18.383	24.013	39.571
beta3_pelagic[5]	30.141	8.188	18.411	28.772	45.228
beta3_pelagic[6]	31.827	6.734	19.204	31.573	44.198
beta3_pelagic[7]	29.985	8.002	18.446	28.900	45.026
beta3_pelagic[8]	29.480	8.011	18.426	28.119	45.101
beta3_pelagic[9]	30.877	6.160	19.250	30.885	42.975
beta3_pelagic[10]	29.268	8.071	18.415	27.498	44.802
beta3_pelagic[11]	42.451	1.891	37.335	43.012	45.293
beta3_pelagic[12]	43.457	0.283	42.977	43.443	43.951
beta3_pelagic[13]	42.792	1.295	40.255	42.808	45.405
beta3_pelagic[14]	42.282	1.643	38.972	42.280	45.501
beta3_pelagic[15]	43.169	0.285	42.479	43.172	43.729
beta3_pelagic[16]	43.195	0.783	41.267	43.242	45.162
mu_beta0_pelagic[1]	0.642	1.066	-1.682	0.699	2.727
mu_beta0_pelagic[2]	1.807	0.381	1.023	1.812	2.546
mu_beta0_pelagic[3]	0.351	0.476	-0.667	0.363	1.294
tau_beta0_pelagic[1]	0.474	0.524	0.048	0.298	1.973
tau_beta0_pelagic[2]	2.767	3.034	0.283	1.982	9.516
tau_beta0_pelagic[3]	1.583	1.218	0.174	1.254	4.827
beta0_yellow[1]	-0.537	0.192	-0.990	-0.523	-0.219
beta0_yellow[2]	0.494	0.181	0.140	0.507	0.791
beta0_yellow[3]	-0.326	0.197	-0.748	-0.314	0.020
beta0_yellow[4]	0.825	0.316	-0.074	0.883	1.216
beta0_yellow[5]	-0.288	0.353	-1.006	-0.293	0.389
beta0_yellow[6]	1.112	0.167	0.789	1.113	1.428
beta0_yellow[7]	0.985	0.160	0.678	0.981	1.312
beta0_yellow[8]	1.014	0.156	0.705	1.012	1.325
beta0_yellow[9]	0.662	0.157	0.353	0.664	0.972
beta0_yellow[10]	0.589	0.145	0.311	0.590	0.876
beta0_yellow[11]	-1.997	0.456	-2.923	-1.991	-1.126
beta0_yellow[12]	-3.695	0.423	-4.559	-3.673	-2.920
beta0_yellow[13]	-3.722	0.469	-4.700	-3.683	-2.882
beta0_yellow[14]	-2.149	0.509	-3.092	-2.170	-1.109
beta0_yellow[15]	-2.852	0.411	-3.709	-2.833	-2.073
beta0_yellow[16]	-2.410	0.439	-3.256	-2.410	-1.536
beta1_yellow[1]	0.834	1.133	0.009	0.661	2.873
beta1_yellow[2]	1.074	0.395	0.577	1.019	2.150
beta1_yellow[3]	0.714	0.290	0.250	0.696	1.309
beta1_yellow[4]	1.368	0.778	0.639	1.164	3.873
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	2.142	0.452	1.253	2.138	3.068
beta1_yellow[12]	2.486	0.433	1.701	2.456	3.405
beta1_yellow[13]	2.836	0.469	2.016	2.807	3.865
beta1_yellow[14]	2.221	0.505	1.175	2.228	3.179
beta1_yellow[15]	2.099	0.416	1.314	2.086	2.961
beta1_yellow[16]	2.172	0.440	1.324	2.167	3.043
beta2_yellow[1]	-4.010	3.449	-12.301	-3.107	-0.053
beta2_yellow[2]	-3.820	3.313	-12.359	-2.914	-0.183
beta2_yellow[3]	-4.204	3.807	-13.140	-3.049	-0.144
beta2_yellow[4]	-3.422	3.362	-12.066	-2.402	-0.090
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.745	2.861	-11.977	-4.133	-1.106
beta2_yellow[12]	-5.062	2.806	-12.200	-4.446	-1.381
beta2_yellow[13]	-4.880	2.604	-11.609	-4.283	-1.555
beta2_yellow[14]	-4.979	2.937	-12.128	-4.432	-0.725
beta2_yellow[15]	-4.505	2.815	-11.587	-3.876	-1.023
beta2_yellow[16]	-5.112	2.775	-11.864	-4.523	-1.354
beta3_yellow[1]	25.727	7.016	18.296	22.749	44.366
beta3_yellow[2]	29.098	1.831	25.514	28.875	32.917
beta3_yellow[3]	32.949	3.165	25.088	32.899	39.697
beta3_yellow[4]	29.135	3.511	21.993	28.023	35.962
beta3_yellow[5]	29.875	7.987	18.449	28.785	44.804
beta3_yellow[6]	29.846	7.988	18.460	28.732	44.879
beta3_yellow[7]	30.180	7.980	18.410	29.434	45.055
beta3_yellow[8]	30.215	7.998	18.539	29.179	45.051
beta3_yellow[9]	30.208	7.958	18.540	29.289	44.970
beta3_yellow[10]	30.126	7.932	18.515	29.353	44.977
beta3_yellow[11]	45.298	0.681	44.071	45.411	45.973
beta3_yellow[12]	43.299	0.403	42.546	43.280	44.022
beta3_yellow[13]	44.876	0.394	44.000	44.950	45.559
beta3_yellow[14]	44.201	1.362	42.944	44.273	45.856
beta3_yellow[15]	45.156	0.531	44.148	45.140	45.961
beta3_yellow[16]	44.553	0.652	43.394	44.538	45.826
mu_beta0_yellow[1]	0.094	0.563	-1.046	0.091	1.220
mu_beta0_yellow[2]	0.642	0.335	-0.090	0.660	1.284
mu_beta0_yellow[3]	-2.456	0.644	-3.465	-2.553	-0.878
tau_beta0_yellow[1]	1.884	3.310	0.092	1.188	7.429
tau_beta0_yellow[2]	3.489	4.285	0.317	2.266	14.663
tau_beta0_yellow[3]	1.490	2.147	0.099	0.927	5.908
beta0_black[1]	-0.074	0.158	-0.386	-0.075	0.230
beta0_black[2]	1.915	0.128	1.660	1.914	2.167
beta0_black[3]	1.315	0.136	1.053	1.312	1.586
beta0_black[4]	2.427	0.135	2.167	2.428	2.691
beta0_black[5]	4.626	2.077	1.799	4.183	9.980
beta0_black[6]	4.628	1.931	2.223	4.170	9.462
beta0_black[7]	3.779	1.938	1.503	3.273	9.124
beta0_black[8]	0.952	0.208	0.549	0.956	1.361
beta0_black[9]	2.609	0.232	2.135	2.614	3.060
beta0_black[10]	1.457	0.136	1.194	1.455	1.716
beta0_black[11]	3.482	0.151	3.179	3.483	3.777
beta0_black[12]	4.868	0.173	4.522	4.867	5.206
beta0_black[13]	-0.109	0.255	-0.600	-0.099	0.341
beta0_black[14]	2.851	0.159	2.545	2.851	3.162
beta0_black[15]	1.294	0.154	0.987	1.299	1.583
beta0_black[16]	4.274	0.162	3.956	4.277	4.595
beta2_black[1]	7.584	9.763	0.558	3.413	38.782
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-2.181	1.757	-6.979	-1.633	-0.407
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.748	1.310	39.719	41.942	43.221
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.249	0.820	37.464	39.337	40.615
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.262	0.196	-0.640	-0.260	0.125
beta4_black[2]	0.239	0.184	-0.126	0.239	0.594
beta4_black[3]	-0.934	0.197	-1.330	-0.933	-0.558
beta4_black[4]	0.421	0.219	0.006	0.417	0.850
beta4_black[5]	0.551	1.283	-1.353	0.361	3.532
beta4_black[6]	0.514	1.210	-1.378	0.311	3.655
beta4_black[7]	0.449	1.225	-1.282	0.260	3.298
beta4_black[8]	-0.234	0.310	-0.831	-0.234	0.387
beta4_black[9]	0.855	0.791	-0.269	0.712	2.741
beta4_black[10]	0.051	0.184	-0.312	0.051	0.412
beta4_black[11]	-0.691	0.214	-1.101	-0.693	-0.260
beta4_black[12]	0.165	0.321	-0.442	0.155	0.822
beta4_black[13]	-1.189	0.226	-1.643	-1.184	-0.763
beta4_black[14]	-0.175	0.232	-0.623	-0.178	0.274
beta4_black[15]	-0.891	0.216	-1.321	-0.890	-0.467
beta4_black[16]	-0.594	0.231	-1.049	-0.592	-0.140
mu_beta0_black[1]	1.323	0.888	-0.531	1.337	3.125
mu_beta0_black[2]	2.724	1.077	0.726	2.624	5.236
mu_beta0_black[3]	2.528	0.974	0.443	2.567	4.414
tau_beta0_black[1]	0.643	0.624	0.057	0.457	2.297
tau_beta0_black[2]	0.447	0.647	0.046	0.240	2.050
tau_beta0_black[3]	0.241	0.162	0.050	0.200	0.666
beta0_dsr[11]	-2.889	0.298	-3.474	-2.895	-2.288
beta0_dsr[12]	4.546	0.331	4.000	4.548	5.129
beta0_dsr[13]	-1.352	0.314	-1.954	-1.345	-0.786
beta0_dsr[14]	-3.661	0.511	-4.672	-3.661	-2.666
beta0_dsr[15]	-1.936	0.281	-2.498	-1.936	-1.370
beta0_dsr[16]	-2.995	0.365	-3.716	-2.994	-2.266
beta1_dsr[11]	4.823	0.311	4.196	4.824	5.431
beta1_dsr[12]	6.846	12.398	2.209	4.982	19.316
beta1_dsr[13]	2.858	0.332	2.286	2.849	3.469
beta1_dsr[14]	6.323	0.534	5.292	6.327	7.400
beta1_dsr[15]	3.333	0.288	2.761	3.332	3.897
beta1_dsr[16]	5.807	0.385	5.054	5.814	6.557
beta2_dsr[11]	-8.312	2.391	-14.139	-7.970	-4.710
beta2_dsr[12]	-7.148	2.734	-13.321	-6.947	-2.361
beta2_dsr[13]	-6.487	2.752	-12.623	-6.304	-1.654
beta2_dsr[14]	-6.199	2.718	-12.045	-6.021	-1.833
beta2_dsr[15]	-7.802	2.510	-13.750	-7.464	-3.850
beta2_dsr[16]	-7.877	2.305	-13.094	-7.634	-4.185
beta3_dsr[11]	43.491	0.153	43.214	43.486	43.780
beta3_dsr[12]	33.966	0.741	32.116	34.120	34.819
beta3_dsr[13]	43.248	0.310	42.797	43.189	43.882
beta3_dsr[14]	43.343	0.236	43.071	43.271	43.951
beta3_dsr[15]	43.504	0.187	43.172	43.498	43.852
beta3_dsr[16]	43.436	0.157	43.171	43.421	43.747
beta4_dsr[11]	0.589	0.224	0.168	0.588	1.030
beta4_dsr[12]	0.249	0.437	-0.630	0.240	1.112
beta4_dsr[13]	-0.165	0.224	-0.621	-0.164	0.264
beta4_dsr[14]	0.155	0.246	-0.343	0.158	0.648
beta4_dsr[15]	0.725	0.216	0.315	0.723	1.149
beta4_dsr[16]	0.156	0.231	-0.309	0.159	0.609
beta0_slope[11]	-1.842	0.144	-2.119	-1.843	-1.558
beta0_slope[12]	-4.464	0.256	-4.966	-4.459	-3.962
beta0_slope[13]	-1.338	0.187	-1.761	-1.326	-1.019
beta0_slope[14]	-2.674	0.165	-2.996	-2.671	-2.358
beta0_slope[15]	-1.342	0.143	-1.628	-1.339	-1.060
beta0_slope[16]	-2.736	0.159	-3.043	-2.738	-2.421
beta1_slope[11]	4.488	0.216	4.066	4.486	4.908
beta1_slope[12]	3.996	0.445	3.130	3.998	4.839
beta1_slope[13]	2.726	0.484	2.188	2.643	4.221
beta1_slope[14]	6.314	0.426	5.488	6.314	7.174
beta1_slope[15]	3.011	0.207	2.626	3.002	3.425
beta1_slope[16]	5.293	0.279	4.773	5.294	5.828
beta2_slope[11]	8.694	2.344	5.147	8.330	14.052
beta2_slope[12]	6.720	2.850	1.269	6.722	12.734
beta2_slope[13]	5.393	3.078	0.389	5.342	11.919
beta2_slope[14]	6.371	2.514	2.256	6.211	11.999
beta2_slope[15]	8.281	2.450	4.555	7.896	14.101
beta2_slope[16]	7.822	2.287	4.315	7.528	13.120
beta3_slope[11]	43.463	0.138	43.210	43.459	43.734
beta3_slope[12]	43.356	0.278	42.890	43.318	43.943
beta3_slope[13]	43.471	0.396	42.941	43.421	44.077
beta3_slope[14]	43.267	0.133	43.097	43.234	43.600
beta3_slope[15]	43.492	0.161	43.192	43.495	43.794
beta3_slope[16]	43.379	0.147	43.156	43.355	43.705
beta4_slope[11]	-0.736	0.164	-1.066	-0.734	-0.421
beta4_slope[12]	-1.166	0.458	-2.167	-1.130	-0.387
beta4_slope[13]	0.085	0.159	-0.236	0.088	0.388
beta4_slope[14]	-0.093	0.193	-0.466	-0.091	0.279
beta4_slope[15]	-0.763	0.155	-1.076	-0.758	-0.457
beta4_slope[16]	-0.164	0.176	-0.509	-0.165	0.177
sigma_H[1]	0.201	0.054	0.105	0.198	0.317
sigma_H[2]	0.171	0.030	0.118	0.169	0.233
sigma_H[3]	0.197	0.044	0.118	0.194	0.289
sigma_H[4]	0.423	0.076	0.296	0.415	0.592
sigma_H[5]	0.999	0.205	0.623	0.987	1.421
sigma_H[6]	0.442	0.194	0.065	0.435	0.826
sigma_H[7]	0.310	0.066	0.206	0.301	0.469
sigma_H[8]	0.412	0.086	0.267	0.403	0.605
sigma_H[9]	0.527	0.128	0.327	0.506	0.819
sigma_H[10]	0.211	0.042	0.139	0.208	0.304
sigma_H[11]	0.276	0.045	0.201	0.272	0.378
sigma_H[12]	0.436	0.168	0.207	0.410	0.782
sigma_H[13]	0.213	0.037	0.148	0.210	0.292
sigma_H[14]	0.509	0.094	0.345	0.501	0.710
sigma_H[15]	0.247	0.041	0.177	0.243	0.339
sigma_H[16]	0.226	0.045	0.155	0.222	0.330
lambda_H[1]	3.299	4.365	0.158	1.891	14.679
lambda_H[2]	8.122	7.594	0.787	5.829	29.231
lambda_H[3]	6.665	10.678	0.270	3.403	31.875
lambda_H[4]	0.006	0.004	0.001	0.005	0.017
lambda_H[5]	4.188	11.266	0.037	1.066	27.607
lambda_H[6]	8.279	15.961	0.008	1.273	53.272
lambda_H[7]	0.013	0.009	0.002	0.010	0.035
lambda_H[8]	8.611	10.733	0.148	4.894	39.587
lambda_H[9]	0.015	0.010	0.003	0.013	0.040
lambda_H[10]	0.290	0.470	0.032	0.195	1.111
lambda_H[11]	0.251	0.348	0.010	0.120	1.270
lambda_H[12]	4.667	6.215	0.182	2.731	20.891
lambda_H[13]	3.466	3.076	0.252	2.575	12.100
lambda_H[14]	3.229	3.743	0.222	2.023	13.518
lambda_H[15]	0.026	0.043	0.003	0.017	0.098
lambda_H[16]	0.774	1.003	0.041	0.423	3.700
mu_lambda_H[1]	4.417	1.890	1.346	4.242	8.614
mu_lambda_H[2]	3.929	1.963	0.627	3.824	8.105
mu_lambda_H[3]	3.507	1.876	0.722	3.226	7.675
sigma_lambda_H[1]	8.697	4.240	2.242	8.131	18.008
sigma_lambda_H[2]	8.542	4.666	1.067	8.052	18.305
sigma_lambda_H[3]	6.296	4.008	0.927	5.422	16.111
beta_H[1,1]	6.900	1.066	4.430	7.055	8.517
beta_H[2,1]	9.876	0.498	8.788	9.902	10.779
beta_H[3,1]	7.998	0.764	6.182	8.083	9.209
beta_H[4,1]	9.351	7.792	-7.100	9.534	24.191
beta_H[5,1]	0.135	2.273	-4.682	0.318	3.905
beta_H[6,1]	3.258	3.906	-6.948	4.700	7.458
beta_H[7,1]	0.634	5.914	-12.157	1.090	11.027
beta_H[8,1]	1.328	3.349	-2.149	1.257	3.454
beta_H[9,1]	13.094	5.651	2.003	13.041	24.443
beta_H[10,1]	6.987	1.696	3.297	7.100	10.180
beta_H[11,1]	4.916	3.575	-3.071	5.651	9.855
beta_H[12,1]	2.636	1.068	0.743	2.575	5.056
beta_H[13,1]	9.036	0.913	7.128	9.111	10.525
beta_H[14,1]	2.169	1.022	0.118	2.175	4.222
beta_H[15,1]	-6.099	3.858	-12.933	-6.393	2.144
beta_H[16,1]	3.480	2.657	-0.806	3.089	9.758
beta_H[1,2]	7.914	0.242	7.404	7.917	8.389
beta_H[2,2]	10.026	0.133	9.759	10.026	10.287
beta_H[3,2]	8.950	0.200	8.566	8.948	9.358
beta_H[4,2]	3.581	1.495	0.808	3.521	6.646
beta_H[5,2]	1.946	0.941	0.043	1.965	3.701
beta_H[6,2]	5.736	1.028	3.219	5.911	7.334
beta_H[7,2]	2.657	1.114	0.600	2.566	5.024
beta_H[8,2]	3.035	1.015	1.508	3.142	4.266
beta_H[9,2]	3.484	1.105	1.382	3.449	5.750
beta_H[10,2]	8.203	0.342	7.479	8.210	8.843
beta_H[11,2]	9.808	0.642	8.850	9.703	11.232
beta_H[12,2]	3.951	0.370	3.253	3.935	4.697
beta_H[13,2]	9.124	0.252	8.664	9.110	9.639
beta_H[14,2]	4.022	0.352	3.349	4.012	4.726
beta_H[15,2]	11.365	0.699	9.872	11.415	12.631
beta_H[16,2]	4.522	0.821	2.969	4.521	6.166
beta_H[1,3]	8.447	0.240	8.015	8.432	8.948
beta_H[2,3]	10.065	0.119	9.823	10.065	10.286
beta_H[3,3]	9.611	0.166	9.288	9.612	9.955
beta_H[4,3]	-2.520	0.870	-4.329	-2.502	-0.841
beta_H[5,3]	3.842	0.590	2.649	3.847	4.991
beta_H[6,3]	7.895	1.183	6.335	7.513	10.479
beta_H[7,3]	-2.791	0.663	-4.090	-2.784	-1.521
beta_H[8,3]	5.237	0.476	4.640	5.186	6.100
beta_H[9,3]	-2.859	0.743	-4.288	-2.839	-1.408
beta_H[10,3]	8.678	0.277	8.137	8.679	9.225
beta_H[11,3]	8.525	0.291	7.896	8.550	9.034
beta_H[12,3]	5.245	0.324	4.492	5.287	5.763
beta_H[13,3]	8.847	0.175	8.489	8.851	9.182
beta_H[14,3]	5.708	0.279	5.113	5.727	6.197
beta_H[15,3]	10.364	0.319	9.760	10.360	10.989
beta_H[16,3]	6.252	0.593	4.927	6.312	7.229
beta_H[1,4]	8.262	0.179	7.884	8.275	8.572
beta_H[2,4]	10.127	0.118	9.881	10.131	10.337
beta_H[3,4]	10.119	0.163	9.760	10.130	10.408
beta_H[4,4]	11.791	0.453	10.862	11.792	12.653
beta_H[5,4]	5.492	0.739	4.326	5.413	7.200
beta_H[6,4]	7.033	0.923	4.947	7.306	8.243
beta_H[7,4]	8.278	0.350	7.586	8.286	8.917
beta_H[8,4]	6.717	0.244	6.286	6.724	7.145
beta_H[9,4]	7.200	0.469	6.274	7.191	8.123
beta_H[10,4]	7.730	0.234	7.274	7.723	8.218
beta_H[11,4]	9.392	0.202	8.997	9.387	9.777
beta_H[12,4]	7.149	0.210	6.742	7.147	7.558
beta_H[13,4]	9.045	0.144	8.760	9.046	9.337
beta_H[14,4]	7.734	0.220	7.297	7.733	8.167
beta_H[15,4]	9.467	0.240	8.987	9.471	9.932
beta_H[16,4]	9.343	0.238	8.919	9.331	9.840
beta_H[1,5]	8.989	0.143	8.692	8.995	9.255
beta_H[2,5]	10.783	0.093	10.613	10.781	10.977
beta_H[3,5]	10.909	0.170	10.605	10.900	11.263
beta_H[4,5]	8.403	0.471	7.518	8.398	9.382
beta_H[5,5]	5.430	0.563	4.147	5.477	6.390
beta_H[6,5]	8.822	0.636	7.904	8.668	10.314
beta_H[7,5]	6.752	0.345	6.094	6.741	7.472
beta_H[8,5]	8.219	0.212	7.866	8.207	8.616
beta_H[9,5]	8.207	0.471	7.278	8.220	9.158
beta_H[10,5]	10.095	0.221	9.662	10.100	10.530
beta_H[11,5]	11.505	0.227	11.057	11.507	11.962
beta_H[12,5]	8.483	0.199	8.099	8.480	8.903
beta_H[13,5]	10.012	0.129	9.761	10.012	10.266
beta_H[14,5]	9.203	0.232	8.774	9.193	9.684
beta_H[15,5]	11.165	0.246	10.682	11.166	11.657
beta_H[16,5]	9.926	0.180	9.548	9.932	10.264
beta_H[1,6]	10.176	0.181	9.867	10.163	10.580
beta_H[2,6]	11.514	0.105	11.307	11.513	11.714
beta_H[3,6]	10.821	0.156	10.483	10.831	11.101
beta_H[4,6]	12.860	0.826	11.157	12.868	14.398
beta_H[5,6]	5.894	0.609	4.733	5.902	7.112
beta_H[6,6]	8.848	0.671	7.020	8.982	9.777
beta_H[7,6]	9.854	0.572	8.697	9.864	10.974
beta_H[8,6]	9.522	0.270	9.025	9.543	9.951
beta_H[9,6]	8.442	0.783	6.915	8.446	10.025
beta_H[10,6]	9.514	0.312	8.842	9.531	10.078
beta_H[11,6]	10.814	0.359	10.026	10.843	11.467
beta_H[12,6]	9.377	0.261	8.883	9.369	9.924
beta_H[13,6]	11.049	0.167	10.762	11.042	11.403
beta_H[14,6]	9.818	0.292	9.233	9.817	10.390
beta_H[15,6]	10.838	0.428	9.971	10.839	11.655
beta_H[16,6]	10.530	0.243	10.028	10.541	10.980
beta_H[1,7]	10.899	0.851	8.780	11.000	12.273
beta_H[2,7]	12.207	0.442	11.252	12.218	13.058
beta_H[3,7]	10.549	0.658	9.036	10.622	11.609
beta_H[4,7]	2.551	4.218	-5.601	2.463	11.085
beta_H[5,7]	6.409	1.874	3.025	6.368	10.450
beta_H[6,7]	9.776	2.410	5.094	9.676	16.262
beta_H[7,7]	10.567	2.877	4.764	10.586	16.235
beta_H[8,7]	10.941	0.935	9.553	10.911	12.463
beta_H[9,7]	4.533	4.005	-3.437	4.498	12.302
beta_H[10,7]	9.820	1.455	7.189	9.731	13.029
beta_H[11,7]	10.981	1.731	7.843	10.879	14.828
beta_H[12,7]	9.960	0.965	7.681	10.067	11.573
beta_H[13,7]	11.645	0.761	9.871	11.752	12.790
beta_H[14,7]	10.362	0.954	8.318	10.406	12.050
beta_H[15,7]	12.003	2.245	7.705	11.983	16.712
beta_H[16,7]	12.330	1.295	10.227	12.168	15.327
beta0_H[1]	9.273	12.446	-15.392	9.212	35.608
beta0_H[2]	10.574	6.605	-2.768	10.550	24.079
beta0_H[3]	9.956	9.672	-10.571	10.137	29.239
beta0_H[4]	4.998	191.126	-375.756	10.112	396.274
beta0_H[5]	3.934	23.346	-41.631	4.368	46.359
beta0_H[6]	7.235	47.177	-109.259	7.636	110.218
beta0_H[7]	7.500	138.320	-265.319	6.437	282.446
beta0_H[8]	7.311	28.131	-15.780	6.483	29.583
beta0_H[9]	9.169	119.766	-220.615	7.608	253.209
beta0_H[10]	10.100	33.518	-53.630	9.411	81.537
beta0_H[11]	9.982	51.324	-94.841	9.309	118.430
beta0_H[12]	6.740	11.417	-15.723	6.656	30.561
beta0_H[13]	10.065	10.744	-9.070	9.731	34.091
beta0_H[14]	6.879	11.533	-17.489	7.069	29.383
beta0_H[15]	10.289	107.165	-203.575	8.716	227.795
beta0_H[16]	7.309	25.818	-46.443	7.888	60.218